Understanding and Creating Switchable Many-State Architectured Materials Through the Exploitation of Nonlinear Post-Buckling Behavior

Architectured materials consist of two or more constituent materials and empty space arranged in and ordered assembly. These materials have properties not offered by any one material alone. One class of relevant materials is that of lattice materials where periodic assemblies of slender material elements make up the material's internal structure. When subjected to mechanical loads, these materials can respond in extremely complex and highly nonlinear ways. The response often includes buckling of the microstructure elements. During this instability the microstructure changes from one configuration to another. This award supports fundamental research to generate the knowledge necessary to understand and design architectured materials with desirable types of microlevel buckling behavior. These materials would be switchable between many different buckled states, and each state would have its own properties that could be tailored for specific applications. Such materials would have many applications ranging from vibration control in aerospace structures with multiple flight regimes to multi-function sensors where, for example, one material state would sense changes in magnetic field, another changes in temperature, and a third changes in mechanical load. The research project will train graduate and undergraduate students in the emerging science of architectured materials and the mechanics of buckling and instabilities. It will also encourage participation of underrepresented groups in research and engineering through the incorporation of research results in graduate and undergraduate courses at the University of Minnesota, and through interaction with K-12 faculty and students.

The project will research the fundamental issue of post-buckling behavior in periodic architectured materials. Research will be conducted on the nonlinear mathematical modeling and characterization of buckling and instabilities in the microstructure of architectured materials; on the high-performance computational simulation of these complex materials; and on understanding how the behavior of these materials is affected by the presence of imperfections in their constituent materials and/or their manufacture. The research will employ the mathematical theories of bifurcation and symmetry groups to understand the complex buckling mechanisms that occur in periodic architectured materials. It will use these mathematical tools to explore and create computational algorithms for efficiently and systematically mapping out the rich set of states and buckling behavior associated with these materials. The research will also study how a periodic architectured material's buckling behavior depends on its periodic unit cell properties such as size, shape, lattice geometry, and constituent material properties.